The Boundedness of Calderón–Zygmund Operators on Lipschitz Spaces Over Spaces of Homogeneous Type

Abstract

Let $$(\mathcal {X},\rho ,\mu )$$ be Ahlfors-1 regular metric spaces. By developing the Littlewood–Paley characterization of Lipschitz spaces over $$(\mathcal {X},\rho ,\mu )$$ and establishing a density argument in the weak sense, the authors give a necessary and sufficient condition for the boundedness of Calderon–Zygmund operators on the Lipschitz spaces.